Plot hole: As Dale comes to Hank's work and talks to Hank about the gun incident he has a spray pack on his back that is filled with poison and by accident sprays Joe Jack. Yet in the episode "The Exterminator" Dale was told by the doctors that he would not be able to use any type of hazardous chemicals with bug spraying as his lungs wouldn't be able to handle the fumes any more. Even if he ignored the advice the chemicals would have at least incapacitated him or killed him.
Character mistake: When Peggy and Lupe return to Mexico and Peggy thinks the crowd of people are cheering her on, she says "Por los niños!", pronouncing the "ñ" correctly. However, in several other episodes of the show, she pronounces the "ñ" in the word "español" incorrectly.
Other mistake: The premise of this episode makes no sense. Bobby and Connie have previously spent a lot of time together and/or with Joseph. They were also shown on "dates", i.e. the high school dance where No Doubt played. Basically, they were a steady junior high/middle school couple. However, in this episode, they are suddenly "too different" and can barely get through a few dates together.
Deliberate mistake: The Olympic symbol (of 5 inter-connected rings) is upside-down on the tracksuits the torch carriers are wearing near the end of the episode. It has 3 rings at the top, not 2.
Deliberate mistake: After Peggy has knocked King Philip off his horse at the end you can the sun is setting behind her, when it goes to a reaction shot of Bobby and Luann in the stands, it is a blue sky and sunny behind them. The following shot of Peggy it goes back to the sun setting. The mistake could be said to be deliberate as the shot was used earlier in the scene and probably used again to save time and money than re-animating the exact same shot.
Continuity mistake: After Peggy throws the tomato at King Philip you see it lands on the badge on his jacket. Most of the tomato lands about the top of his badge and seems to set on the top part. A few scenes later when Peggy is being put in the stocks for punishment you see Philip again and the stain has moved down the badge. Most notably the tomato stain looks larger and a large chunk of it has moved below the badge onto the shirt.
Continuity mistake: When Hank and the family are approaching Cotton's table at the rummage sale, there are two empty knife sheathes and one sheathed knife on his table. In the next shot, there are 3 sheathes and 2 knives out of the sheathes. (00:03:25)
Continuity mistake: When Hank's trying to convince his dad to let the Vietnam vets join the VFW, the table behind him with the bowl of fruit and the vase of flowers on it disappears between shots. (00:12:45 - 00:13:15)
Continuity mistake: When Hank's trying to convince his dad to let the Vietnam vets join the VFW, the table behind him with the bowl of fruit and the vase of flowers on it disappears between shots. (00:12:45 - 00:13:15)
Other mistake: At the prison, Bill meets Alicia, the same woman who gave Leanne a ride to the Hill house in Season Two ("Leanne's Saga"). Same voice, tattoo on the arm, and general appearance. Alicia tells him that she was in prison for killing her boyfriend. So it's odd that she was free in Season Two. Most likely, a sentence for homicide or manslaughter would be at least five years, and that much time has not passed. Otherwise, Bobby, Connie, and Joseph would be in their late teens.
Returning Japanese (1) - S6-E21
Plot hole: In this episode, Hank meets his paternal half brother. They look alike. However, we saw in an earlier episode that Hank's facial structure takes after his mother, not his father. Since they are paternal half brothers, then the Japanese brother cannot look like Hank since he has a different mother.
Returning Japanese (1) - S6-E21
Factual error: As the Hills get off the plane in Japan the camera crew is waiting for them as they exit the terminal however they do not go through any sort of customs area. Every international flight you must go through customs before entering the country.
Returning Japanese (1) - S6-E21
Continuity mistake: On the plane whilst Bobby is watching the TV in front of him, you can see a man to the left of Bobby and an empty seat to Bobby's right. The seat arrangement looks to be like the middle row of seats where there is 3 seats instead of two. After the shot shows footage for the "Haiku" movie the shot changes to Bobby and the man sitting next to him but there is now no empty seat next to Bobby. It appears that he is now sitting at a window seat.
Returning Japanese (1) - S6-E21
Factual error: During the scenes where the Hills arrive at the airport in Japan, there is no flight crew outside or around the terminal when they exit. Whilst they may be the last people to exit the plane, there will be one or more crew members to farewell passengers and also to close the terminal door. There doesn't seem to be any crew anywhere close, which seems particularly odd especially as Hank and Cotton manage to just stroll back onto the plane. A little after they leave the camera crew just go right through the terminal onto the plane without anyone there to stop them.
Returning Japanese (1) - S6-E21
Factual error: In the airport scene in Japan, the news crew arrives to film Cotton Hill. As Cotton Hill gets back on the plane trying to escape the news crew, we see a shot from outside the plane and the news crew is out on the tarmac. With security regulations at airports a film crew wouldn't be allowed to just go out onto the tarmac.
Answer: If you are talking about the "Thou shalt not do this, thou shalt not do that" song, I'm not sure if a song like that actually exists. Green Day, the guest voices on the episode, might have just been improvising to keep their appearance from being too obvious.